On the generalized Cochrane sum with Dirichlet characters

• DOI: 10.3934/math.20231542
• Publication Date: 2023-11-07T11:40:15Z
• Authors: Jiankang Wang; Zhefeng Xu; Minmin Jia
• Keywords: dirichlet character; QA1-939; upper bound; mean value; Mathematics; generalized cochrane sum

<abstract><p>In this paper, we defined a new generalized Cochrane sum with Dirichlet characters, and gave the upper bound of the generalized Cochrane sum with Dirichlet characters. Moreover, we studied the asymptotic estimation problem of the mean value of the generalized Cochrane sum with Dirichlet characters and obtained a sharp asymptotic formula for it. By using this asymptotic formula, we also gave the mean value of the generalized Dedekind sum.</p></abstract>